The Saturation Function of Complete Partite Graphs

A graph G is called \emph{F-saturated} if it is F-free but theaddition of any missing edge to G creates a copy of F.Let the saturation function \sat(n,F) be the minimum numberof edges that an F-saturated graph on n vertices can have.We determine this function asymptotically forevery fixed complete partite graph F as n tends to infinity andgive some structural information aboutalmost extremal F-saturated graphs.If the two largest parts of F have different sizes,then we can reduce the error term to an additive constant.